Oliver C. Ibe

Fundamentals of Stochastic Networks (eBook, PDF)

• Format: PDF

Produktbeschreibung

An interdisciplinary approach to understanding queueing and graphical networks In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physical sciences. The author uniquely unites different types of stochastic, queueing, and graphical networks that are typically studied independently of each other. With balanced coverage, the book is organized into three succinct parts: * Part I introduces basic concepts in probability and stochastic processes, with coverage on counting, Poisson, renewal, and Markov processes * Part II addresses basic queueing theory, with a focus on Markovian queueing systems and also explores advanced queueing theory, queueing networks, and approximations of queueing networks * Part III focuses on graphical models, presenting an introduction to graph theory along with Bayesian, Boolean, and random networks The author presents the material in a self-contained style that helps readers apply the presented methods and techniques to science and engineering applications. Numerous practical examples are also provided throughout, including all related mathematical details. Featuring basic results without heavy emphasis on proving theorems, Fundamentals of Stochastic Networks is a suitable book for courses on probability and stochastic networks, stochastic network calculus, and stochastic network optimization at the upper-undergraduate and graduate levels. The book also serves as a reference for researchers and network professionals who would like to learn more about the general principles of stochastic networks.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 312
• Erscheinungstermin: 24. August 2011
• Englisch
• ISBN-13: 9781118092996
• Artikelnr.: 37486653

Autorenporträt

OLIVER C. IBE, ScD, is Associate Professor in the Department of Electrical and Computer Engineering at the University of Massachusetts at Lowell. He has more than thirty years of experience in academia and the telecommunications industry in various technical and management capacities. Dr. Ibe's research interests include stochastic systems modeling, bioinformatics, and communication network performance modeling. He is the author of Converged Network Architectures: Delivering Voice over IP, ATM, and Frame Relay (Wiley).

Inhaltsangabe

Preface xi Acknowledgments
xii 1 Basic Concepts in Probability 1 1.1 Introduction
1 1.2 Random Variables
1 1.3 Transform Methods
5 1.4 Covariance and Correlation Coefficient
8 1.5 Sums of Independent Random Variables
8 1.6 Random Sum of Random Variables
9 1.7 Some Probability Distributions
11 1.8 Limit Theorems
21 2 Overview of Stochastic Processes 26 2.1 Introduction
26 2.2 Classification of Stochastic Processes
27 2.3 Stationary Random Processes
27 2.4 Counting Processes
28 2.5 Independent Increment Processes
29 2.6 Stationary Increment Process
29 2.7 Poisson Processes
30 2.8 Renewal Processes
32 2.9 Markov Processes
37 2.10 Gaussian Processes
56 3 Elementary Queueing Theory 61 3.1 Introduction
61 3.2 Description of a Queueing System
61 3.3 The Kendall Notation
64 3.4 The Little's Formula
65 3.5 The M/M/1 Queueing System
66 3.6 Examples of Other M/M Queueing Systems
71 3.7 M/G/1 Queue
79 4 Advanced Queueing Theory 93 4.1 Introduction
93 4.2 M/G/1 Queue with Priority
93 4.3 G/M/1 Queue
99 4.4 The G/G/1 Queue
105 4.5 Special Queueing Systems
109 5 Queueing Networks 124 5.1 Introduction
124 5.2 Burke's Output Theorem and Tandem Queues
126 5.3 Jackson or Open Queueing Networks
128 5.4 Closed Queueing Networks
130 5.5 BCMP Networks
132 5.6 Algorithms for Product-Form Queueing Networks
138 5.7 Networks with Positive and Negative Customers
144 6 Approximations of Queueing Systems and Networks 150 6.1 Introduction
150 6.2 Fluid Approximation
151 6.3 Diffusion Approximations
155 7 Elements of Graph Theory 172 7.1 Introduction
172 7.2 Basic Concepts
172 7.3 Connected Graphs
177 7.4 Cut Sets
Bridges
and Cut Vertices
177 7.5 Euler Graphs
178 7.6 Hamiltonian Graphs
178 7.7 Trees and Forests
179 7.8 Minimum Weight Spanning Trees
181 7.9 Bipartite Graphs and Matchings
182 7.10 Independent Set
Domination
and Covering
186 7.11 Complement of a Graph
188 7.12 Isomorphic Graphs
188 7.13 Planar Graphs
189 7.14 Graph Coloring
191 7.14.1 Edge Coloring
191 7.14.2 The Four-Color Problem
192 7.15 Random Graphs
192 7.16 Matrix Algebra of Graphs
195 7.17 Spectral Properties of Graphs
198 7.18 Graph Entropy
201 7.19 Directed Acyclic Graphs
201 7.20 Moral Graphs
202 7.21 Triangulated Graphs
202 7.22 Chain Graphs
203 7.23 Factor Graphs
204 8 Bayesian Networks 209 8.1 Introduction
209 8.2 Bayesian Networks
210 8.3 Classification of BNs
214 8.4 General Conditional Independence and d-Separation
215 8.5 Probabilistic Inference in BNs
215 8.6 Learning BNs
227 8.7 Dynamic Bayesian Networks
231 9 Boolean Networks 235 9.1 Introduction
235 9.2 Introduction to GRNs
236 9.3 Boolean Network Basics
236 9.4 Random Boolean Networks
238 9.5 State Transition Diagram
239 9.6 Behavior of Boolean Networks
240 9.7 Petri Net Analysis of Boolean Networks
242 9.8 Probabilistic Boolean Networks
250 9.9 Dynamics of a PBN
251 9.10 Advantages and Disadvantages of Boolean Networks
252 10 Random Networks 255 10.1 Introduction
255 10.2 Characterization of Complex Networks
256 10.3 Models of Complex Networks
261 10.4 Random Networks
265 10.5 Random Regular Networks
267 10.6 Consensus over Random Networks
268 10.7 Summary
274 References 276 Index 280